1. Inability to apply to asexual organisms: The biological species concept defines a species as a group of organisms that can interbreed and produce fertile offspring. Asexual organisms, like bacteria and some plants, reproduce without mating, so this concept doesn't apply to them. Determining species boundaries in these organisms requires other methods like genetic analysis.

2. Difficulties in application to hybridizing species: Some species can interbreed and produce fertile offspring, even though they are considered distinct species. This is common in plants, and also occurs in some animals. For example, the gray wolf and the coyote can interbreed, making it challenging to apply the biological species concept in these cases. This ambiguity can lead to disagreement about where one species ends and another begins.